Multiple choice

Passage

Directions: Based on the following information, answer the following question. On 9 th October, 2021, it rained heavily throughout the day over the city of Punjab. Mr. Deshraj observed that each of the raindrops which reached him was in the shape of a hemisphere surmounted by a cone of the same radius of 1.5 mm and the volume of one of such raindrop was 3.75π mm 3 . Deshraj collected the rainwater in a vessel having a capacity of 2355 cm 3 . (Use π = 3.14)

Find the curved surface area of a raindrop.

  1. 26 mm2

  2. 22 mm2

  3. 36 mm2

  4. 28 mm2

  5. None of these
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A Correct answer
Explanation

Volume = 3.75 * pi = 2/3 * pi * r^3 + 1/3 * pi * r^2 * h. r = 1.5. 3.75 = 2/3 * (1.5)^3 + 1/3 * (1.5)^2 * h. 3.75 = 2.25 + 0.75 * h. 1.5 = 0.75 * h => h = 2. CSA = 2 * pi * r^2 + pi * r * l. l = sqrt(r^2 + h^2) = sqrt(2.25 + 4) = 2.5. CSA = 2 * pi * 2.25 + pi * 1.5 * 2.5 = 4.5 * pi + 3.75 * pi = 8.25 * pi = 8.25 * 3.14 = 25.905, approx 26.

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